Application of fuzzy preference modelling to the fusion of sensory profile data P.-A. H´ ebert * , M.-H. Masson † , T. Denœux * , P. Faye ‡ , S. Millemann ‡ and C. Egoroff ‡ * Universit´ e de Technologie de Compi` egne Heudiasyc - UMR CNRS 6599 BP 20529 - F-60205 Compi` egne Cedex - France Email: hebert@hds.utc.fr † Universit´ e de Picardie Jules Vernes Heudiasyc - UMR CNRS 6599 BP 20529 - F-60205 Compi` egne Cedex - France ‡ PSA Peugeot Citro¨ en PErception et Facteurs Humains DRIA/SARA/STEV/PEFH 2 route de Gisy 78943 V´ elizy-Villacoublay - France Abstract— We propose a new analysis method to deal with sensory profile data. Such data are composed of scores attributed by human experts (or judges) in order to describe a set of products according to a given sensory descriptor. All assessments are repeated, usually three times. The first step consists in extracting and encoding the relevant information of each replicate into a fuzzy weak dominance relation. Then an aggregation procedure over the replicates allows synthesis of the perception of each judge into a new fuzzy relation. In a similar way, a consensual relation is finally obtained by fusing the relations of the judges. The proposed analysis tools are based on a particular objective of the fuzzy preference modelling: the decomposition of a fuzzy weak preference relation into a fuzzy preference structure. An example of application illustrates the interest of the method. Index Terms— sensory profile data analysis, fuzzy logic, fuzzy preference modelling, aggregation. I. I NTRODUCTION A. Sensory profile data analysis We focus in this paper on sensory profile data, i.e., data gathered from a group of persons, in order to describe the way they perceive a set of products according to a given sensory descriptor. Acquisition is managed according to the following protocol: in the course of n r spaced screenings, a panel of n j persons called judges evaluate each one of the n p products according to the descriptor, by giving a score u pjr ∈ [0, 10]. These values are asserted using a graphical user interface, by moving a cursor on to a continuous finite scale. The main objective of sensory profile data analysis is to describe how the products are perceived by the judges. But it has also to describe the own performances of the judges, notably their ability to replicate their scores and to be discriminant. A more global performance indicator can then be provided for the panel, in order to measure the agreement of the judges. A particular difficulty of such data is due to the imprecision of the assessments. In spite of training, a perfect similarity among the n r replicates is not plausible. For this reason, the analysis clearly needs to take into account this imprecision. A common solution consists in averaging the scores over the replicates and applying an analysis of variance. We claim that this approach is not completely suitable. Fundamentally, we may consider that each judge does not exactly assert the same information during the n r replicates. On the one hand, if two products are only slightly different, their difference may or may not be perceived. Indeed, we may reasonably suppose that the ability of a judge to discriminate the products is not constant, especially when the products are almost similar. On the other hand, the evaluation of the intensity of a sensation is difficult, and the judge may deliver erroneous scores. In these two situations, the differences between the scores of two products should not be necessarily understood as a difference of intensity. Averaging the scores could be suitable for a large number of replicates, but only three replicates are generally available. Based on a compromise between a quantitative and an or- dinal approach, the proposed method uses a radically different way of fusing sensory profile data, first over the replicates to summarize the perception of each judge, and then over the judges so as to express a consensus. 0-7803-9286-8/05/$20.00 © 2005 IEEE